LMFDB - Embedded newform 800.2.bq.d.223.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.6
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.d.287.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.751816 + 1.47552i) q^{3} +(-0.850652 + 2.06794i) q^{5} +(0.0884893 + 0.0884893i) q^{7} +(0.151419 - 0.208410i) q^{9} +(1.38554 + 1.90703i) q^{11} +(0.276048 + 1.74290i) q^{13} +(-3.69083 + 0.299558i) q^{15} +(-0.750646 - 0.382473i) q^{17} +(1.22753 + 3.77794i) q^{19} +(-0.0640402 + 0.197096i) q^{21} +(-0.800533 + 5.05437i) q^{23} +(-3.55278 - 3.51820i) q^{25} +(5.32824 + 0.843910i) q^{27} +(-4.81698 - 1.56513i) q^{29} +(-1.45130 + 0.471555i) q^{31} +(-1.77220 + 3.47813i) q^{33} +(-0.258265 + 0.107717i) q^{35} +(-4.99237 + 0.790713i) q^{37} +(-2.36415 + 1.71766i) q^{39} +(-1.45307 - 1.05572i) q^{41} +(-1.67304 + 1.67304i) q^{43} +(0.302175 + 0.490409i) q^{45} +(-1.13972 + 0.580715i) q^{47} -6.98434i q^{49} -1.39514i q^{51} +(-8.95574 + 4.56318i) q^{53} +(-5.12225 + 1.24300i) q^{55} +(-4.65156 + 4.65156i) q^{57} +(7.48107 + 5.43532i) q^{59} +(8.45057 - 6.13970i) q^{61} +(0.0318410 - 0.00504312i) q^{63} +(-3.83904 - 0.911749i) q^{65} +(6.31654 - 12.3969i) q^{67} +(-8.05968 + 2.61875i) q^{69} +(4.67813 + 1.52002i) q^{71} +(3.90231 + 0.618064i) q^{73} +(2.52014 - 7.88725i) q^{75} +(-0.0461465 + 0.291358i) q^{77} +(-0.526155 + 1.61934i) q^{79} +(2.52183 + 7.76139i) q^{81} +(2.73237 + 1.39221i) q^{83} +(1.42947 - 1.22694i) q^{85} +(-1.31210 - 8.28425i) q^{87} +(-6.16660 - 8.48760i) q^{89} +(-0.129801 + 0.178655i) q^{91} +(-1.78690 - 1.78690i) q^{93} +(-8.85676 - 0.675253i) q^{95} +(6.36605 + 12.4941i) q^{97} +0.607241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43}+ \cdots + 132 q^{99}+O(q^{100}) $ 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.751816	+	1.47552i	0.434061	+	0.851893i	0.999630	+	0.0271920i	$0.00865653\pi$
$3$	0.751816	+	1.47552i	0.434061	+	0.851893i	−0.565569	+	0.824701i	$0.691343\pi$
$4$		0			0
$5$	−0.850652	+	2.06794i	−0.380423	+	0.924813i
$5$	−0.850652	+	2.06794i	−0.380423	+	0.924813i
$6$		0			0
$7$	0.0884893	+	0.0884893i	0.0334458	+	0.0334458i	0.723632	−	0.690186i	$-0.242471\pi$
$7$	0.0884893	+	0.0884893i	0.0334458	+	0.0334458i	−0.690186	+	0.723632i	$0.742471\pi$
$8$		0			0
$9$	0.151419	−	0.208410i	0.0504729	−	0.0694700i
$10$		0			0
$11$	1.38554	+	1.90703i	0.417756	+	0.574992i	0.965089	−	0.261923i	$-0.0843567\pi$
$11$	1.38554	+	1.90703i	0.417756	+	0.574992i	−0.547333	+	0.836915i	$0.684357\pi$
$12$		0			0
$13$	0.276048	+	1.74290i	0.0765620	+	0.483394i	0.995940	+	0.0900186i	$0.0286926\pi$
$13$	0.276048	+	1.74290i	0.0765620	+	0.483394i	−0.919378	+	0.393375i	$0.871307\pi$
$14$		0			0
$15$	−3.69083	+	0.299558i	−0.952968	+	0.0773456i
$16$		0			0
$17$	−0.750646	−	0.382473i	−0.182058	−	0.0927634i	0.360586	−	0.932726i	$-0.382577\pi$
$17$	−0.750646	−	0.382473i	−0.182058	−	0.0927634i	−0.542644	+	0.839963i	$0.682577\pi$
$18$		0			0
$19$	1.22753	+	3.77794i	0.281614	+	0.866718i	0.987393	+	0.158287i	$0.0505970\pi$
$19$	1.22753	+	3.77794i	0.281614	+	0.866718i	−0.705779	+	0.708432i	$0.749403\pi$
$20$		0			0
$21$	−0.0640402	+	0.197096i	−0.0139747	+	0.0430098i
$22$		0			0
$23$	−0.800533	+	5.05437i	−0.166923	+	1.05391i	0.751911	+	0.659264i	$0.229132\pi$
$23$	−0.800533	+	5.05437i	−0.166923	+	1.05391i	−0.918834	+	0.394644i	$0.870868\pi$
$24$		0			0
$25$	−3.55278	−	3.51820i	−0.710557	−	0.703640i
$26$		0			0
$27$	5.32824	+	0.843910i	1.02542	+	0.162411i
$28$		0			0
$29$	−4.81698	−	1.56513i	−0.894491	−	0.290638i	−0.174529	−	0.984652i	$-0.555840\pi$
$29$	−4.81698	−	1.56513i	−0.894491	−	0.290638i	−0.719961	+	0.694014i	$0.755840\pi$
$30$		0			0
$31$	−1.45130	+	0.471555i	−0.260661	+	0.0846938i	−0.436432	−	0.899737i	$-0.643758\pi$
$31$	−1.45130	+	0.471555i	−0.260661	+	0.0846938i	0.175771	+	0.984431i	$0.443758\pi$
$32$		0			0
$33$	−1.77220	+	3.47813i	−0.308500	+	0.605465i
$34$		0			0
$35$	−0.258265	+	0.107717i	−0.0436547	+	0.0182076i
$36$		0			0
$37$	−4.99237	+	0.790713i	−0.820740	+	0.129992i	−0.552663	−	0.833405i	$-0.686388\pi$
$37$	−4.99237	+	0.790713i	−0.820740	+	0.129992i	−0.268077	+	0.963397i	$0.586388\pi$
$38$		0			0
$39$	−2.36415	+	1.71766i	−0.378567	+	0.275045i
$40$		0			0
$41$	−1.45307	−	1.05572i	−0.226931	−	0.164875i	0.468510	−	0.883458i	$-0.344791\pi$
$41$	−1.45307	−	1.05572i	−0.226931	−	0.164875i	−0.695441	+	0.718583i	$0.744791\pi$
$42$		0			0
$43$	−1.67304	+	1.67304i	−0.255136	+	0.255136i	−0.823073	−	0.567936i	$-0.807742\pi$
$43$	−1.67304	+	1.67304i	−0.255136	+	0.255136i	0.567936	+	0.823073i	$0.307742\pi$
$44$		0			0
$45$	0.302175	+	0.490409i	0.0450457	+	0.0731059i
$46$		0			0
$47$	−1.13972	+	0.580715i	−0.166245	+	0.0847059i	−0.535133	−	0.844768i	$-0.679739\pi$
$47$	−1.13972	+	0.580715i	−0.166245	+	0.0847059i	0.368888	+	0.929474i	$0.379739\pi$
$48$		0			0
$49$		−	6.98434i		−	0.997763i
$50$		0			0
$51$		−	1.39514i		−	0.195359i
$52$		0			0
$53$	−8.95574	+	4.56318i	−1.23017	+	0.626801i	−0.943545	−	0.331244i	$-0.892532\pi$
$53$	−8.95574	+	4.56318i	−1.23017	+	0.626801i	−0.286620	+	0.958044i	$0.592532\pi$
$54$		0			0
$55$	−5.12225	+	1.24300i	−0.690684	+	0.167606i
$56$		0			0
$57$	−4.65156	+	4.65156i	−0.616114	+	0.616114i
$58$		0			0
$59$	7.48107	+	5.43532i	0.973952	+	0.707618i	0.956349	−	0.292227i	$-0.0943963\pi$
$59$	7.48107	+	5.43532i	0.973952	+	0.707618i	0.0176035	+	0.999845i	$0.494396\pi$
$60$		0			0
$61$	8.45057	−	6.13970i	1.08199	−	0.786108i	0.103957	−	0.994582i	$-0.466850\pi$
$61$	8.45057	−	6.13970i	1.08199	−	0.786108i	0.978028	+	0.208474i	$0.0668495\pi$
$62$		0			0
$63$	0.0318410	−	0.00504312i	0.00401159	−	0.000635373i
$64$		0			0
$65$	−3.83904	−	0.911749i	−0.476175	−	0.113089i
$66$		0			0
$67$	6.31654	−	12.3969i	0.771688	−	1.51452i	−0.0836745	−	0.996493i	$-0.526666\pi$
$67$	6.31654	−	12.3969i	0.771688	−	1.51452i	0.855363	−	0.518030i	$-0.173334\pi$
$68$		0			0
$69$	−8.05968	+	2.61875i	−0.970271	+	0.315260i
$70$		0			0
$71$	4.67813	+	1.52002i	0.555192	+	0.180393i	0.573157	−	0.819446i	$-0.305719\pi$
$71$	4.67813	+	1.52002i	0.555192	+	0.180393i	−0.0179646	+	0.999839i	$0.505719\pi$
$72$		0			0
$73$	3.90231	+	0.618064i	0.456730	+	0.0723390i	0.380561	−	0.924756i	$-0.375731\pi$
$73$	3.90231	+	0.618064i	0.456730	+	0.0723390i	0.0761695	+	0.997095i	$0.475731\pi$
$74$		0			0
$75$	2.52014	−	7.88725i	0.291001	−	0.910741i
$76$		0			0
$77$	−0.0461465	+	0.291358i	−0.00525888	+	0.0332033i
$78$		0			0
$79$	−0.526155	+	1.61934i	−0.0591971	+	0.182190i	−0.976282	−	0.216501i	$-0.930535\pi$
$79$	−0.526155	+	1.61934i	−0.0591971	+	0.182190i	0.917085	+	0.398691i	$0.130535\pi$
$80$		0			0
$81$	2.52183	+	7.76139i	0.280203	+	0.862377i
$82$		0			0
$83$	2.73237	+	1.39221i	0.299916	+	0.152815i	0.597473	−	0.801889i	$-0.296172\pi$
$83$	2.73237	+	1.39221i	0.299916	+	0.152815i	−0.297557	+	0.954704i	$0.596172\pi$
$84$		0			0
$85$	1.42947	−	1.22694i	0.155048	−	0.133081i
$86$		0			0
$87$	−1.31210	−	8.28425i	−0.140671	−	0.888165i
$88$		0			0
$89$	−6.16660	−	8.48760i	−0.653658	−	0.899683i	0.345593	−	0.938385i	$-0.387678\pi$
$89$	−6.16660	−	8.48760i	−0.653658	−	0.899683i	−0.999251	+	0.0387013i	$0.987678\pi$
$90$		0			0
$91$	−0.129801	+	0.178655i	−0.0136068	+	0.0187282i
$92$		0			0
$93$	−1.78690	−	1.78690i	−0.185293	−	0.185293i
$94$		0			0
$95$	−8.85676	−	0.675253i	−0.908685	−	0.0692795i
$96$		0			0
$97$	6.36605	+	12.4941i	0.646374	+	1.26858i	0.948941	+	0.315452i	$0.102156\pi$
$97$	6.36605	+	12.4941i	0.646374	+	1.26858i	−0.302567	+	0.953128i	$0.597844\pi$
$98$		0			0
$99$	0.607241			0.0610300
$100$		0			0
$101$	18.5616			1.84694			0.923472	−	0.383665i	$-0.125338\pi$
$101$	18.5616			1.84694			0.923472	+	0.383665i	$0.125338\pi$
$102$		0			0
$103$	4.58370	+	8.99601i	0.451645	+	0.886403i	0.998781	+	0.0493595i	$0.0157180\pi$
$103$	4.58370	+	8.99601i	0.451645	+	0.886403i	−0.547136	+	0.837044i	$0.684282\pi$
$104$		0			0
$105$	−0.353107	−	0.300091i	−0.0344597	−	0.0292859i
$106$		0			0
$107$	11.1361	+	11.1361i	1.07657	+	1.07657i	0.996814	+	0.0797564i	$0.0254142\pi$
$107$	11.1361	+	11.1361i	1.07657	+	1.07657i	0.0797564	+	0.996814i	$0.474586\pi$
$108$		0			0
$109$	4.32607	−	5.95432i	0.414362	−	0.570321i	−0.549913	−	0.835222i	$-0.685339\pi$
$109$	4.32607	−	5.95432i	0.414362	−	0.570321i	0.964276	+	0.264901i	$0.0853393\pi$
$110$		0			0
$111$	−4.92005	−	6.77187i	−0.466991	−	0.642758i
$112$		0			0
$113$	2.06649	+	13.0473i	0.194399	+	1.22739i	0.871090	+	0.491123i	$0.163413\pi$
$113$	2.06649	+	13.0473i	0.194399	+	1.22739i	−0.676691	+	0.736267i	$0.736587\pi$
$114$		0			0
$115$	−9.77117	−	5.95496i	−0.911166	−	0.555303i
$116$		0			0
$117$	0.405037	+	0.206376i	0.0374456	+	0.0190795i
$118$		0			0
$119$	−0.0325794	−	0.100269i	−0.00298655	−	0.00919164i
$120$		0			0
$121$	1.68214	−	5.17708i	0.152921	−	0.470644i
$122$		0			0
$123$	0.465292	−	2.93774i	0.0419540	−	0.264887i
$124$		0			0
$125$	10.2976	−	4.35420i	0.921047	−	0.389451i
$126$		0			0
$127$	−6.35597	−	1.00669i	−0.564001	−	0.0893290i	−0.132078	−	0.991239i	$-0.542165\pi$
$127$	−6.35597	−	1.00669i	−0.564001	−	0.0893290i	−0.431923	+	0.901910i	$0.642165\pi$
$128$		0			0
$129$	−3.72643	−	1.21079i	−0.328093	−	0.106604i
$130$		0			0
$131$	−6.16164	+	2.00204i	−0.538345	+	0.174919i	−0.565555	−	0.824711i	$-0.691338\pi$
$131$	−6.16164	+	2.00204i	−0.538345	+	0.174919i	0.0272096	+	0.999630i	$0.491338\pi$
$132$		0			0
$133$	−0.225684	+	0.442930i	−0.0195693	+	0.0384069i
$134$		0			0
$135$	−6.27763	+	10.3006i	−0.540293	+	0.886536i
$136$		0			0
$137$	6.99200	−	1.10742i	0.597366	−	0.0946136i	0.149573	−	0.988751i	$-0.452210\pi$
$137$	6.99200	−	1.10742i	0.597366	−	0.0946136i	0.447793	+	0.894137i	$0.352210\pi$
$138$		0			0
$139$	−6.09420	+	4.42770i	−0.516903	+	0.375552i	−0.815436	−	0.578847i	$-0.803503\pi$
$139$	−6.09420	+	4.42770i	−0.516903	+	0.375552i	0.298533	+	0.954399i	$0.403503\pi$
$140$		0			0
$141$	−1.71371	−	1.24509i	−0.144321	−	0.104855i
$142$		0			0
$143$	−2.94129	+	2.94129i	−0.245963	+	0.245963i
$144$		0			0
$145$	7.33417	−	8.62986i	0.609070	−	0.716671i
$146$		0			0
$147$	10.3055	−	5.25094i	0.849987	−	0.433090i
$148$		0			0
$149$			4.13678i			0.338898i	0.985539	+	0.169449i	$0.0541988\pi$
$149$			4.13678i			0.338898i	−0.985539	+	0.169449i	$0.945801\pi$
$150$		0			0
$151$		−	16.8476i		−	1.37104i	−0.728054	−	0.685520i	$-0.759575\pi$
$151$		−	16.8476i		−	1.37104i	0.728054	−	0.685520i	$-0.240425\pi$
$152$		0			0
$153$	−0.193373	+	0.0985285i	−0.0156333	+	0.00796556i
$154$		0			0
$155$	0.259399	−	3.40233i	0.0208354	−	0.273282i
$156$		0			0
$157$	15.7245	−	15.7245i	1.25495	−	1.25495i	0.301482	−	0.953472i	$-0.402519\pi$
$157$	15.7245	−	15.7245i	1.25495	−	1.25495i	0.953472	−	0.301482i	$-0.0974812\pi$
$158$		0			0
$159$	−13.4661	−	9.78372i	−1.06793	−	0.775899i
$160$		0			0
$161$	−0.518096	+	0.376419i	−0.0408317	+	0.0296660i
$162$		0			0
$163$	1.72689	−	0.273513i	0.135261	−	0.0214232i	−0.0884370	−	0.996082i	$-0.528187\pi$
$163$	1.72689	−	0.273513i	0.135261	−	0.0214232i	0.223698	+	0.974659i	$0.428187\pi$
$164$		0			0
$165$	−5.68506	−	6.62348i	−0.442581	−	0.515637i
$166$		0			0
$167$	3.14209	−	6.16669i	0.243142	−	0.477193i	−0.736895	−	0.676007i	$-0.763709\pi$
$167$	3.14209	−	6.16669i	0.243142	−	0.477193i	0.980037	+	0.198814i	$0.0637090\pi$
$168$		0			0
$169$	9.40223	−	3.05497i	0.723249	−	0.234998i
$170$		0			0
$171$	0.973230	+	0.316222i	0.0744248	+	0.0241821i
$172$		0			0
$173$	−7.07140	−	1.12000i	−0.537629	−	0.0851521i	−0.118285	−	0.992980i	$-0.537740\pi$
$173$	−7.07140	−	1.12000i	−0.537629	−	0.0851521i	−0.419344	+	0.907828i	$0.637740\pi$
$174$		0			0
$175$	−0.00306035	−	0.625707i	−0.000231341	−	0.0472990i
$176$		0			0
$177$	−2.39554	+	15.1248i	−0.180060	+	1.13685i
$178$		0			0
$179$	−5.75913	+	17.7248i	−0.430458	+	1.32481i	0.467212	+	0.884145i	$0.345258\pi$
$179$	−5.75913	+	17.7248i	−0.430458	+	1.32481i	−0.897670	+	0.440668i	$0.854742\pi$
$180$		0			0
$181$	1.65404	+	5.09060i	0.122944	+	0.378381i	0.993521	−	0.113650i	$-0.0362544\pi$
$181$	1.65404	+	5.09060i	0.122944	+	0.378381i	−0.870577	+	0.492032i	$0.836254\pi$
$182$		0			0
$183$	15.4125	+	7.85308i	1.13933	+	0.580516i
$184$		0			0
$185$	2.61161	−	10.9966i	0.192010	−	0.808483i
$186$		0			0
$187$	−0.310661	−	1.96144i	−0.0227178	−	0.143435i
$188$		0			0
$189$	0.396815	+	0.546169i	0.0288641	+	0.0397280i
$190$		0			0
$191$	13.9854	−	19.2493i	1.01195	−	1.39283i	0.0942529	−	0.995548i	$-0.469954\pi$
$191$	13.9854	−	19.2493i	1.01195	−	1.39283i	0.917697	−	0.397281i	$-0.130046\pi$
$192$		0			0
$193$	−2.31934	−	2.31934i	−0.166949	−	0.166949i	0.618688	−	0.785637i	$-0.287665\pi$
$193$	−2.31934	−	2.31934i	−0.166949	−	0.166949i	−0.785637	+	0.618688i	$0.787665\pi$
$194$		0			0
$195$	−1.54095	−	6.35006i	−0.110350	−	0.454737i
$196$		0			0
$197$	7.18858	+	14.1084i	0.512165	+	1.00518i	0.991810	+	0.127718i	$0.0407653\pi$
$197$	7.18858	+	14.1084i	0.512165	+	1.00518i	−0.479645	+	0.877462i	$0.659235\pi$
$198$		0			0
$199$	−10.7082			−0.759082			−0.379541	−	0.925175i	$-0.623918\pi$
$199$	−10.7082			−0.759082			−0.379541	+	0.925175i	$0.623918\pi$
$200$		0			0
$201$	23.0408			1.62517
$202$		0			0
$203$	−0.287754	−	0.564749i	−0.0201964	−	0.0396376i
$204$		0			0
$205$	3.41922	−	2.10682i	0.238808	−	0.147147i
$206$		0			0
$207$	0.932164	+	0.932164i	0.0647899	+	0.0647899i
$208$		0			0
$209$	−5.50386	+	7.57542i	−0.380710	+	0.524003i
$210$		0			0
$211$	−16.5073	−	22.7204i	−1.13641	−	1.56414i	−0.775277	−	0.631622i	$-0.782390\pi$
$211$	−16.5073	−	22.7204i	−1.13641	−	1.56414i	−0.361134	−	0.932514i	$-0.617610\pi$
$212$		0			0
$213$	1.27428	+	8.04546i	0.0873119	+	0.551266i
$214$		0			0
$215$	−2.03658	−	4.88293i	−0.138894	−	0.333013i
$216$		0			0
$217$	−0.170152	−	0.0866967i	−0.0115507	−	0.00588536i
$218$		0			0
$219$	2.02185	+	6.22261i	0.136624	+	0.420485i
$220$		0			0
$221$	0.459398	−	1.41388i	0.0309025	−	0.0951081i
$222$		0			0
$223$	0.997631	−	6.29880i	0.0668063	−	0.421799i	−0.931506	−	0.363726i	$-0.881504\pi$
$223$	0.997631	−	6.29880i	0.0668063	−	0.421799i	0.998312	−	0.0580727i	$-0.0184955\pi$
$224$		0			0
$225$	−1.27119	+	0.207714i	−0.0847457	+	0.0138476i
$226$		0			0
$227$	2.56132	+	0.405672i	0.170000	+	0.0269254i	0.240854	−	0.970561i	$-0.422572\pi$
$227$	2.56132	+	0.405672i	0.170000	+	0.0269254i	−0.0708539	+	0.997487i	$0.522572\pi$
$228$		0			0
$229$	−1.73971	−	0.565265i	−0.114963	−	0.0373537i	0.250971	−	0.967995i	$-0.419250\pi$
$229$	−1.73971	−	0.565265i	−0.114963	−	0.0373537i	−0.365934	+	0.930641i	$0.619250\pi$
$230$		0			0
$231$	−0.464598	+	0.150957i	−0.0305683	+	0.00993225i
$232$		0			0
$233$	3.61760	−	7.09993i	0.236997	−	0.465132i	−0.741621	−	0.670819i	$-0.765943\pi$
$233$	3.61760	−	7.09993i	0.236997	−	0.465132i	0.978618	+	0.205687i	$0.0659428\pi$
$234$		0			0
$235$	−0.231383	−	2.85086i	−0.0150938	−	0.185969i
$236$		0			0
$237$	−2.78494	+	0.441092i	−0.180901	+	0.0286520i
$238$		0			0
$239$	6.94065	−	5.04268i	0.448953	−	0.326184i	−0.340229	−	0.940343i	$-0.610505\pi$
$239$	6.94065	−	5.04268i	0.448953	−	0.326184i	0.789182	+	0.614159i	$0.210505\pi$
$240$		0			0
$241$	−16.1939	−	11.7656i	−1.04314	−	0.757887i	−0.0722456	−	0.997387i	$-0.523017\pi$
$241$	−16.1939	−	11.7656i	−1.04314	−	0.757887i	−0.970896	+	0.239500i	$0.923017\pi$
$242$		0			0
$243$	1.88764	−	1.88764i	0.121092	−	0.121092i
$244$		0			0
$245$	14.4432	+	5.94124i	0.922744	+	0.379572i
$246$		0			0
$247$	−6.24571	+	3.18235i	−0.397405	+	0.202488i
$248$		0			0
$249$			5.07835i			0.321827i
$250$		0			0
$251$		−	12.4024i		−	0.782835i	−0.920213	−	0.391417i	$-0.871985\pi$
$251$		−	12.4024i		−	0.782835i	0.920213	−	0.391417i	$-0.128015\pi$
$252$		0			0
$253$	−10.7480	+	5.47638i	−0.675722	+	0.344297i
$254$		0			0
$255$	2.88508	+	1.18678i	0.180671	+	0.0743192i
$256$		0			0
$257$	6.77274	−	6.77274i	0.422472	−	0.422472i	−0.463582	−	0.886054i	$-0.653436\pi$
$257$	6.77274	−	6.77274i	0.422472	−	0.422472i	0.886054	+	0.463582i	$0.153436\pi$
$258$		0			0
$259$	−0.511741	−	0.371801i	−0.0317980	−	0.0231026i
$260$		0			0
$261$	−1.05557	+	0.766916i	−0.0653381	+	0.0474709i
$262$		0			0
$263$	31.8308	−	5.04150i	1.96277	−	0.310872i	0.963738	−	0.266849i	$-0.0859826\pi$
$263$	31.8308	−	5.04150i	1.96277	−	0.310872i	0.999031	−	0.0440228i	$-0.0140174\pi$
$264$		0			0
$265$	−1.81818	−	22.4016i	−0.111690	−	1.37612i
$266$		0			0
$267$	7.88748	−	15.4801i	0.482706	−	0.947364i
$268$		0			0
$269$	−16.0880	+	5.22729i	−0.980900	+	0.318714i	−0.755208	−	0.655485i	$-0.772464\pi$
$269$	−16.0880	+	5.22729i	−0.980900	+	0.318714i	−0.225692	+	0.974199i	$0.572464\pi$
$270$		0			0
$271$	29.5240	+	9.59293i	1.79345	+	0.582729i	0.999675	−	0.0254774i	$-0.00811058\pi$
$271$	29.5240	+	9.59293i	1.79345	+	0.582729i	0.793779	+	0.608206i	$0.208111\pi$
$272$		0			0
$273$	−0.361196	−	0.0572079i	−0.0218606	−	0.00346238i
$274$		0			0
$275$	1.78680	−	11.6499i	0.107748	−	0.702514i
$276$		0			0
$277$	−3.11302	+	19.6549i	−0.187043	+	1.18095i	0.698230	+	0.715874i	$0.253971\pi$
$277$	−3.11302	+	19.6549i	−0.187043	+	1.18095i	−0.885273	+	0.465072i	$0.846029\pi$
$278$		0			0
$279$	−0.121477	+	0.373867i	−0.00727262	+	0.0223828i
$280$		0			0
$281$	−0.893100	−	2.74868i	−0.0532779	−	0.163973i	0.920877	−	0.389853i	$-0.127474\pi$
$281$	−0.893100	−	2.74868i	−0.0532779	−	0.163973i	−0.974155	+	0.225880i	$0.927474\pi$
$282$		0			0
$283$	−28.1099	−	14.3227i	−1.67096	−	0.851396i	−0.993240	−	0.116076i	$-0.962969\pi$
$283$	−28.1099	−	14.3227i	−1.67096	−	0.851396i	−0.677719	−	0.735321i	$-0.737031\pi$
$284$		0			0
$285$	−5.66230	−	13.5760i	−0.335406	−	0.804173i
$286$		0			0
$287$	−0.0351614	−	0.222001i	−0.00207551	−	0.0131043i
$288$		0			0
$289$	−9.57517	−	13.1791i	−0.563245	−	0.775240i
$290$		0			0
$291$	−13.6492	+	18.7865i	−0.800129	+	1.10128i
$292$		0			0
$293$	−10.3449	−	10.3449i	−0.604357	−	0.604357i	0.337109	−	0.941466i	$-0.390551\pi$
$293$	−10.3449	−	10.3449i	−0.604357	−	0.604357i	−0.941466	+	0.337109i	$0.890551\pi$
$294$		0			0
$295$	−17.6037	+	10.8469i	−1.02493	+	0.631529i
$296$		0			0
$297$	5.77312	+	11.3304i	0.334991	+	0.657456i
$298$		0			0
$299$	−9.03024			−0.522232
$300$		0			0
$301$	−0.296092			−0.0170665
$302$		0			0
$303$	13.9549	+	27.3880i	0.801687	+	1.57340i
$304$		0			0
$305$	5.50806	+	22.6981i	0.315391	+	1.29969i
$306$		0			0
$307$	19.8561	+	19.8561i	1.13325	+	1.13325i	0.989633	+	0.143617i	$0.0458733\pi$
$307$	19.8561	+	19.8561i	1.13325	+	1.13325i	0.143617	+	0.989633i	$0.454127\pi$
$308$		0			0
$309$	−9.82771	+	13.5267i	−0.559079	+	0.769506i
$310$		0			0
$311$	−17.7923	−	24.4890i	−1.00891	−	1.38865i	−0.919695	−	0.392633i	$-0.871564\pi$
$311$	−17.7923	−	24.4890i	−1.00891	−	1.38865i	−0.0892151	−	0.996012i	$-0.528436\pi$
$312$		0			0
$313$	−1.83280	−	11.5718i	−0.103596	−	0.654079i	−0.983771	−	0.179429i	$-0.942575\pi$
$313$	−1.83280	−	11.5718i	−0.103596	−	0.654079i	0.880175	−	0.474649i	$-0.157425\pi$
$314$		0			0
$315$	−0.0166567	+	0.0701353i	−0.000938499	+	0.00395168i
$316$		0			0
$317$	2.15472	+	1.09788i	0.121021	+	0.0616633i	0.513453	−	0.858118i	$-0.328366\pi$
$317$	2.15472	+	1.09788i	0.121021	+	0.0616633i	−0.392432	+	0.919781i	$0.628366\pi$
$318$		0			0
$319$	−3.68936	−	11.3547i	−0.206565	−	0.635740i
$320$		0			0
$321$	−8.05929	+	24.8039i	−0.449825	+	1.38442i
$322$		0			0
$323$	0.523523	−	3.30539i	0.0291296	−	0.183917i
$324$		0			0
$325$	5.15113	−	7.16334i	0.285733	−	0.397351i
$326$		0			0
$327$	12.0381	+	1.90665i	0.665711	+	0.105438i
$328$		0			0
$329$	−0.152240	−	0.0494657i	−0.00839325	−	0.00272713i
$330$		0			0
$331$	−19.3863	+	6.29900i	−1.06557	+	0.346224i	−0.788760	−	0.614701i	$-0.789277\pi$
$331$	−19.3863	+	6.29900i	−1.06557	+	0.346224i	−0.276809	+	0.960925i	$0.589277\pi$
$332$		0			0
$333$	−0.591145	+	1.16019i	−0.0323945	+	0.0635778i
$334$		0			0
$335$	20.2629	+	23.6077i	1.10708	+	1.28983i
$336$		0			0
$337$	10.1296	−	1.60437i	0.551796	−	0.0873958i	0.125690	−	0.992070i	$-0.459885\pi$
$337$	10.1296	−	1.60437i	0.551796	−	0.0873958i	0.426105	+	0.904674i	$0.359885\pi$
$338$		0			0
$339$	−17.6980	+	12.8584i	−0.961224	+	0.698370i
$340$		0			0
$341$	−2.91010	−	2.11431i	−0.157591	−	0.114496i
$342$		0			0
$343$	1.23746	−	1.23746i	0.0668168	−	0.0668168i
$344$		0			0
$345$	1.44055	−	18.8946i	0.0775568	−	1.01725i
$346$		0			0
$347$	−23.3969	+	11.9213i	−1.25601	+	0.639969i	−0.950057	−	0.312078i	$-0.898975\pi$
$347$	−23.3969	+	11.9213i	−1.25601	+	0.639969i	−0.305953	+	0.952047i	$0.598975\pi$
$348$		0			0
$349$		−	26.8200i		−	1.43564i	−0.696228	−	0.717821i	$-0.745140\pi$
$349$		−	26.8200i		−	1.43564i	0.696228	−	0.717821i	$-0.254860\pi$
$350$		0			0
$351$			9.51955i			0.508116i
$352$		0			0
$353$	−28.1655	+	14.3511i	−1.49910	+	0.763830i	−0.995006	−	0.0998189i	$-0.968174\pi$
$353$	−28.1655	+	14.3511i	−1.49910	+	0.763830i	−0.504094	+	0.863649i	$0.668174\pi$
$354$		0			0
$355$	−7.12277	+	8.38111i	−0.378037	+	0.444823i
$356$		0			0
$357$	0.123455	−	0.123455i	0.00653395	−	0.00653395i
$358$		0			0
$359$	9.40554	+	6.83352i	0.496405	+	0.360660i	0.807642	−	0.589673i	$-0.200743\pi$
$359$	9.40554	+	6.83352i	0.496405	+	0.360660i	−0.311237	+	0.950332i	$0.600743\pi$
$360$		0			0
$361$	2.60533	−	1.89288i	0.137122	−	0.0996253i
$362$		0			0
$363$	8.90355	−	1.41018i	0.467315	−	0.0740155i
$364$		0			0
$365$	−4.59762	+	7.54399i	−0.240651	+	0.394871i
$366$		0			0
$367$	−13.2366	+	25.9783i	−0.690945	+	1.35606i	0.232602	+	0.972572i	$0.425276\pi$
$367$	−13.2366	+	25.9783i	−0.690945	+	1.35606i	−0.923547	+	0.383485i	$0.874724\pi$
$368$		0			0
$369$	−0.440043	+	0.142979i	−0.0229077	+	0.00744317i
$370$		0			0
$371$	−1.19628	−	0.388695i	−0.0621078	−	0.0201800i
$372$		0			0
$373$	4.33058	+	0.685896i	0.224229	+	0.0355144i	0.267538	−	0.963547i	$-0.413790\pi$
$373$	4.33058	+	0.685896i	0.224229	+	0.0355144i	−0.0433090	+	0.999062i	$0.513790\pi$
$374$		0			0
$375$	14.1666	+	11.9208i	0.731561	+	0.615588i
$376$		0			0
$377$	1.39815	−	8.82757i	0.0720084	−	0.454643i
$378$		0			0
$379$	−2.44158	+	7.51440i	−0.125415	+	0.385989i	−0.993977	−	0.109593i	$-0.965045\pi$
$379$	−2.44158	+	7.51440i	−0.125415	+	0.385989i	0.868561	+	0.495582i	$0.165045\pi$
$380$		0			0
$381$	−3.29313	−	10.1352i	−0.168712	−	0.519243i
$382$		0			0
$383$	6.29625	+	3.20810i	0.321723	+	0.163926i	0.607392	−	0.794402i	$-0.292216\pi$
$383$	6.29625	+	3.20810i	0.321723	+	0.163926i	−0.285669	+	0.958328i	$0.592216\pi$
$384$		0			0
$385$	−0.563256	−	0.343272i	−0.0287062	−	0.0174948i
$386$		0			0
$387$	0.0953486	+	0.602008i	0.00484684	+	0.0306018i
$388$		0			0
$389$	14.3596	+	19.7642i	0.728059	+	1.00209i	0.999217	+	0.0395525i	$0.0125932\pi$
$389$	14.3596	+	19.7642i	0.728059	+	1.00209i	−0.271159	+	0.962535i	$0.587407\pi$
$390$		0			0
$391$	2.53408	−	3.48786i	0.128154	−	0.176389i
$392$		0			0
$393$	−7.58647	−	7.58647i	−0.382687	−	0.382687i
$394$		0			0
$395$	−2.90113	−	2.46555i	−0.145972	−	0.124055i
$396$		0			0
$397$	3.87816	+	7.61132i	0.194639	+	0.382001i	0.967614	−	0.252436i	$-0.0812318\pi$
$397$	3.87816	+	7.61132i	0.194639	+	0.382001i	−0.772974	+	0.634438i	$0.781232\pi$
$398$		0			0
$399$	−0.823226			−0.0412129
$400$		0			0
$401$	7.18801			0.358952			0.179476	−	0.983762i	$-0.442560\pi$
$401$	7.18801			0.358952			0.179476	+	0.983762i	$0.442560\pi$
$402$		0			0
$403$	−1.22250	−	2.39930i	−0.0608972	−	0.119517i
$404$		0			0
$405$	−18.1953	−	1.38724i	−0.904133	−	0.0689325i
$406$		0			0
$407$	−8.42504	−	8.42504i	−0.417614	−	0.417614i
$408$		0			0
$409$	−6.01976	+	8.28549i	−0.297658	+	0.409691i	−0.931483	−	0.363786i	$-0.881484\pi$
$409$	−6.01976	+	8.28549i	−0.297658	+	0.409691i	0.633825	+	0.773477i	$0.281484\pi$
$410$		0			0
$411$	6.89072	+	9.48426i	0.339894	+	0.467824i
$412$		0			0
$413$	0.181027	+	1.14296i	0.00890778	+	0.0562415i
$414$		0			0
$415$	−5.20330	+	4.46609i	−0.255420	+	0.219232i
$416$		0			0
$417$	−11.1149	−	5.66331i	−0.544298	−	0.277334i
$418$		0			0
$419$	10.8890	+	33.5128i	0.531961	+	1.63721i	0.750126	+	0.661295i	$0.229993\pi$
$419$	10.8890	+	33.5128i	0.531961	+	1.63721i	−0.218165	+	0.975912i	$0.570007\pi$
$420$		0			0
$421$	−5.51420	+	16.9710i	−0.268746	+	0.827114i	0.722061	+	0.691829i	$0.243195\pi$
$421$	−5.51420	+	16.9710i	−0.268746	+	0.827114i	−0.990807	+	0.135285i	$0.956805\pi$
$422$		0			0
$423$	−0.0515477	+	0.325459i	−0.00250633	+	0.0158244i
$424$		0			0
$425$	1.32127	+	3.99977i	0.0640908	+	0.194017i
$426$		0			0
$427$	1.29108	+	0.204488i	0.0624799	+	0.00989585i
$428$		0			0
$429$	−6.55125	−	2.12863i	−0.316297	−	0.102771i
$430$		0			0
$431$	15.1614	−	4.92624i	0.730299	−	0.237289i	0.0798164	−	0.996810i	$-0.474567\pi$
$431$	15.1614	−	4.92624i	0.730299	−	0.237289i	0.650483	+	0.759521i	$0.274567\pi$
$432$		0			0
$433$	−3.58768	+	7.04123i	−0.172413	+	0.338380i	−0.961002	−	0.276541i	$-0.910812\pi$
$433$	−3.58768	+	7.04123i	−0.172413	+	0.338380i	0.788589	+	0.614921i	$0.210812\pi$
$434$		0			0
$435$	18.2475	+	4.33367i	0.874900	+	0.207783i
$436$		0			0
$437$	−20.0778	+	3.18000i	−0.960449	+	0.152120i
$438$		0			0
$439$	−6.13149	+	4.45479i	−0.292640	+	0.212615i	−0.724412	−	0.689367i	$-0.757889\pi$
$439$	−6.13149	+	4.45479i	−0.292640	+	0.212615i	0.431772	+	0.901983i	$0.357889\pi$
$440$		0			0
$441$	−1.45561	−	1.05756i	−0.0693145	−	0.0503600i
$442$		0			0
$443$	−23.6674	+	23.6674i	−1.12447	+	1.12447i	−0.133409	+	0.991061i	$0.542592\pi$
$443$	−23.6674	+	23.6674i	−1.12447	+	1.12447i	−0.991061	+	0.133409i	$0.957408\pi$
$444$		0			0
$445$	22.7975	−	5.53220i	1.08071	−	0.262251i
$446$		0			0
$447$	−6.10390	+	3.11009i	−0.288705	+	0.147102i
$448$		0			0
$449$			25.5797i			1.20718i	0.797294	+	0.603591i	$0.206264\pi$
$449$			25.5797i			1.20718i	−0.797294	+	0.603591i	$0.793736\pi$
$450$		0			0
$451$		−	4.23379i		−	0.199361i
$452$		0			0
$453$	24.8590	−	12.6663i	1.16798	−	0.595115i
$454$		0			0
$455$	−0.259034	−	0.420394i	−0.0121437	−	0.0197084i
$456$		0			0
$457$	2.02727	−	2.02727i	0.0948316	−	0.0948316i	−0.658099	−	0.752931i	$-0.728639\pi$
$457$	2.02727	−	2.02727i	0.0948316	−	0.0948316i	0.752931	+	0.658099i	$0.228639\pi$
$458$		0			0
$459$	−3.67685	−	2.67139i	−0.171621	−	0.124690i
$460$		0			0
$461$	−13.1957	+	9.58720i	−0.614583	+	0.446520i	−0.851025	−	0.525125i	$-0.824019\pi$
$461$	−13.1957	+	9.58720i	−0.614583	+	0.446520i	0.236442	+	0.971646i	$0.424019\pi$
$462$		0			0
$463$	5.05924	−	0.801304i	0.235123	−	0.0372398i	−0.0377610	−	0.999287i	$-0.512023\pi$
$463$	5.05924	−	0.801304i	0.235123	−	0.0372398i	0.272884	+	0.962047i	$0.412023\pi$
$464$		0			0
$465$	5.21523	−	2.17518i	0.241851	−	0.100871i
$466$		0			0
$467$	6.08871	−	11.9498i	0.281752	−	0.552969i	−0.706148	−	0.708065i	$-0.749568\pi$
$467$	6.08871	−	11.9498i	0.281752	−	0.552969i	0.987900	+	0.155095i	$0.0495685\pi$
$468$		0			0
$469$	1.65594	−	0.538048i	0.0764642	−	0.0248447i
$470$		0			0
$471$	35.0238	+	11.3799i	1.61381	+	0.524359i
$472$		0			0
$473$	−5.50861	−	0.872478i	−0.253286	−	0.0401166i
$474$		0			0
$475$	8.93040	−	17.7409i	0.409755	−	0.814007i
$476$		0			0
$477$	−0.405055	+	2.55741i	−0.0185462	+	0.117096i
$478$		0			0
$479$	8.71560	−	26.8239i	0.398226	−	1.22561i	−0.528195	−	0.849123i	$-0.677131\pi$
$479$	8.71560	−	26.8239i	0.398226	−	1.22561i	0.926421	−	0.376490i	$-0.122869\pi$
$480$		0			0
$481$	−2.75627	−	8.48292i	−0.125675	−	0.386788i
$482$		0			0
$483$	−0.944927	−	0.481464i	−0.0429957	−	0.0219074i
$484$		0			0
$485$	−31.2523	+	2.53653i	−1.41909	+	0.115178i
$486$		0			0
$487$	−2.00995	−	12.6903i	−0.0910796	−	0.575054i	−0.990451	−	0.137868i	$-0.955975\pi$
$487$	−2.00995	−	12.6903i	−0.0910796	−	0.575054i	0.899371	−	0.437186i	$-0.144025\pi$
$488$		0			0
$489$	1.70188	+	2.34243i	0.0769616	+	0.105929i
$490$		0			0
$491$	−21.8141	+	30.0245i	−0.984455	+	1.35499i	−0.0500604	+	0.998746i	$0.515941\pi$
$491$	−21.8141	+	30.0245i	−0.984455	+	1.35499i	−0.934395	+	0.356240i	$0.884059\pi$
$492$		0			0
$493$	3.01723	+	3.01723i	0.135889	+	0.135889i
$494$		0			0
$495$	−0.516551	+	1.25574i	−0.0232172	+	0.0564413i
$496$		0			0
$497$	0.279459	+	0.548470i	0.0125355	+	0.0246022i
$498$		0			0
$499$	11.5699			0.517938			0.258969	−	0.965886i	$-0.416617\pi$
$499$	11.5699			0.517938			0.258969	+	0.965886i	$0.416617\pi$
$500$		0			0
$501$	11.4614			0.512056
$502$		0			0
$503$	5.09311	+	9.99579i	0.227091	+	0.445690i	0.976234	−	0.216717i	$-0.0695349\pi$
$503$	5.09311	+	9.99579i	0.227091	+	0.445690i	−0.749144	+	0.662407i	$0.769535\pi$
$504$		0			0
$505$	−15.7894	+	38.3843i	−0.702620	+	1.70808i
$506$		0			0
$507$	11.5764	+	11.5764i	0.514127	+	0.514127i
$508$		0			0
$509$	22.0128	−	30.2980i	0.975700	−	1.34294i	0.0365863	−	0.999330i	$-0.488352\pi$
$509$	22.0128	−	30.2980i	0.975700	−	1.34294i	0.939114	−	0.343606i	$-0.111648\pi$
$510$		0			0
$511$	0.290620	+	0.400004i	0.0128563	+	0.0176952i
$512$		0			0
$513$	3.35231	+	21.1657i	0.148008	+	0.934487i
$514$		0			0
$515$	−22.5024	+	1.82636i	−0.991573	+	0.0804789i
$516$		0			0
$517$	−2.68656	−	1.36887i	−0.118155	−	0.0602030i
$518$		0			0
$519$	−3.66381	−	11.2760i	−0.160823	−	0.494963i
$520$		0			0
$521$	0.543009	−	1.67121i	0.0237896	−	0.0732170i	−0.938457	−	0.345396i	$-0.887744\pi$
$521$	0.543009	−	1.67121i	0.0237896	−	0.0732170i	0.962247	+	0.272179i	$0.0877444\pi$
$522$		0			0
$523$	3.45193	−	21.7946i	0.150942	−	0.953012i	−0.789671	−	0.613531i	$-0.789749\pi$
$523$	3.45193	−	21.7946i	0.150942	−	0.953012i	0.940613	−	0.339481i	$-0.110251\pi$
$524$		0			0
$525$	0.920943	−	0.474932i	0.0401932	−	0.0207277i
$526$		0			0
$527$	1.26977	+	0.201112i	0.0553120	+	0.00876056i
$528$		0			0
$529$	−3.03146	−	0.984980i	−0.131802	−	0.0428252i
$530$		0			0
$531$	2.26555	−	0.736121i	0.0983164	−	0.0319449i
$532$		0			0
$533$	1.43889	−	2.82398i	0.0623253	−	0.122320i
$534$		0			0
$535$	−32.5019	+	13.5559i	−1.40518	+	0.586074i
$536$		0			0
$537$	−30.4831	+	4.82805i	−1.31544	+	0.208346i
$538$		0			0
$539$	13.3194	−	9.67708i	0.573706	−	0.416821i
$540$		0			0
$541$	−35.0442	−	25.4611i	−1.50667	−	1.09466i	−0.967629	−	0.252375i	$-0.918788\pi$
$541$	−35.0442	−	25.4611i	−1.50667	−	1.09466i	−0.539037	−	0.842282i	$-0.681212\pi$
$542$		0			0
$543$	−6.26776	+	6.26776i	−0.268975	+	0.268975i
$544$		0			0
$545$	8.63323	+	14.0111i	0.369807	+	0.600171i
$546$		0			0
$547$	12.9757	−	6.61147i	0.554803	−	0.282686i	−0.154026	−	0.988067i	$-0.549224\pi$
$547$	12.9757	−	6.61147i	0.554803	−	0.282686i	0.708829	+	0.705381i	$0.249224\pi$
$548$		0			0
$549$		−	2.69085i		−	0.114843i
$550$		0			0
$551$		−	20.1195i		−	0.857119i
$552$		0			0
$553$	−0.189853	+	0.0967352i	−0.00807339	+	0.00411360i
$554$		0			0
$555$	18.1891	−	4.41389i	0.772084	−	0.187359i
$556$		0			0
$557$	9.69419	−	9.69419i	0.410756	−	0.410756i	−0.471246	−	0.882002i	$-0.656196\pi$
$557$	9.69419	−	9.69419i	0.410756	−	0.410756i	0.882002	+	0.471246i	$0.156196\pi$
$558$		0			0
$559$	−3.37778	−	2.45410i	−0.142865	−	0.103798i
$560$		0			0
$561$	2.66059	−	1.93303i	0.112330	−	0.0816125i
$562$		0			0
$563$	−15.1095	+	2.39311i	−0.636790	+	0.100858i	−0.466478	−	0.884533i	$-0.654477\pi$
$563$	−15.1095	+	2.39311i	−0.636790	+	0.100858i	−0.170312	+	0.985390i	$0.554477\pi$
$564$		0			0
$565$	−28.7390	−	6.82534i	−1.20906	−	0.287144i
$566$		0			0
$567$	−0.463645	+	0.909955i	−0.0194713	+	0.0382145i
$568$		0			0
$569$	−0.345978	+	0.112415i	−0.0145041	+	0.00471268i	−0.316260	−	0.948673i	$-0.602427\pi$
$569$	−0.345978	+	0.112415i	−0.0145041	+	0.00471268i	0.301756	+	0.953385i	$0.402427\pi$
$570$		0			0
$571$	13.3697	+	4.34407i	0.559503	+	0.181794i	0.575098	−	0.818085i	$-0.304964\pi$
$571$	13.3697	+	4.34407i	0.559503	+	0.181794i	−0.0155943	+	0.999878i	$0.504964\pi$
$572$		0			0
$573$	38.9172	+	6.16388i	1.62579	+	0.257500i
$574$		0			0
$575$	20.6264	−	15.1406i	0.860180	−	0.631408i
$576$		0			0
$577$	6.49068	−	40.9806i	0.270211	−	1.70604i	−0.362772	−	0.931878i	$-0.618170\pi$
$577$	6.49068	−	40.9806i	0.270211	−	1.70604i	0.632983	−	0.774166i	$-0.281830\pi$
$578$		0			0
$579$	1.67852	−	5.16594i	0.0697568	−	0.214689i
$580$		0			0
$581$	0.118589	+	0.364981i	0.00491992	+	0.0151420i
$582$		0			0
$583$	−21.1107	−	10.7564i	−0.874314	−	0.445485i
$584$		0			0
$585$	−0.771320	+	0.662039i	−0.0318902	+	0.0273719i
$586$		0			0
$587$	2.66750	+	16.8420i	0.110100	+	0.695142i	0.979562	+	0.201143i	$0.0644655\pi$
$587$	2.66750	+	16.8420i	0.110100	+	0.695142i	−0.869462	+	0.493999i	$0.835535\pi$
$588$		0			0
$589$	−3.56301	−	4.90407i	−0.146811	−	0.202068i
$590$		0			0
$591$	−15.4127	+	21.2138i	−0.633995	+	0.872620i
$592$		0			0
$593$	−8.02300	−	8.02300i	−0.329465	−	0.329465i	0.522918	−	0.852383i	$-0.324843\pi$
$593$	−8.02300	−	8.02300i	−0.329465	−	0.329465i	−0.852383	+	0.522918i	$0.824843\pi$
$594$		0			0
$595$	0.235064	+	0.0179217i	0.00963670	+	0.000734717i
$596$		0			0
$597$	−8.05058	−	15.8001i	−0.329488	−	0.646657i
$598$		0			0
$599$	19.3204			0.789410			0.394705	−	0.918808i	$-0.370847\pi$
$599$	19.3204			0.789410			0.394705	+	0.918808i	$0.370847\pi$
$600$		0			0
$601$	20.9811			0.855837			0.427918	−	0.903817i	$-0.359247\pi$
$601$	20.9811			0.855837			0.427918	+	0.903817i	$0.359247\pi$
$602$		0			0
$603$	−1.62720	−	3.19355i	−0.0662645	−	0.130051i
$604$		0			0
$605$	9.27500	+	7.88245i	0.377082	+	0.320467i
$606$		0			0
$607$	−20.3537	−	20.3537i	−0.826131	−	0.826131i	0.160849	−	0.986979i	$-0.448577\pi$
$607$	−20.3537	−	20.3537i	−0.826131	−	0.826131i	−0.986979	+	0.160849i	$0.948577\pi$
$608$		0			0
$609$	0.616961	−	0.849174i	0.0250005	−	0.0344103i
$610$		0			0
$611$	−1.32674	−	1.82611i	−0.0536743	−	0.0738764i
$612$		0			0
$613$	0.595556	+	3.76019i	0.0240543	+	0.151873i	0.996792	−	0.0800351i	$-0.0255032\pi$
$613$	0.595556	+	3.76019i	0.0240543	+	0.151873i	−0.972738	+	0.231908i	$0.925503\pi$
$614$		0			0
$615$	5.67928	+	3.46119i	0.229010	+	0.139569i
$616$		0			0
$617$	−33.9645	−	17.3058i	−1.36736	−	0.696705i	−0.392549	−	0.919731i	$-0.628407\pi$
$617$	−33.9645	−	17.3058i	−1.36736	−	0.696705i	−0.974812	+	0.223026i	$0.928407\pi$
$618$		0			0
$619$	−11.9890	−	36.8984i	−0.481880	−	1.48307i	−0.836449	−	0.548044i	$-0.815373\pi$
$619$	−11.9890	−	36.8984i	−0.481880	−	1.48307i	0.354570	−	0.935030i	$-0.384627\pi$
$620$		0			0
$621$	−8.53086	+	26.2553i	−0.342332	+	1.05359i
$622$		0			0
$623$	0.205383	−	1.29674i	0.00822851	−	0.0519528i
$624$		0			0
$625$	0.244546	+	24.9988i	0.00978184	+	0.999952i
$626$		0			0
$627$	−15.3156	−	2.42575i	−0.611646	−	0.0968751i
$628$		0			0
$629$	4.04993	+	1.31590i	0.161481	+	0.0524684i
$630$		0			0
$631$	−22.1471	+	7.19602i	−0.881661	+	0.286469i	−0.714647	−	0.699485i	$-0.753413\pi$
$631$	−22.1471	+	7.19602i	−0.881661	+	0.286469i	−0.167014	+	0.985954i	$0.553413\pi$
$632$		0			0
$633$	21.1139	−	41.4385i	0.839204	−	1.64703i
$634$		0			0
$635$	7.48849	−	12.2875i	0.297172	−	0.487613i
$636$		0			0
$637$	12.1730	−	1.92802i	0.482312	−	0.0763908i
$638$		0			0
$639$	1.02514	−	0.744810i	0.0405540	−	0.0294642i
$640$		0			0
$641$	−14.4631	−	10.5080i	−0.571257	−	0.415043i	0.264305	−	0.964439i	$-0.414858\pi$
$641$	−14.4631	−	10.5080i	−0.571257	−	0.415043i	−0.835562	+	0.549397i	$0.814858\pi$
$642$		0			0
$643$	3.35759	−	3.35759i	0.132410	−	0.132410i	−0.637795	−	0.770206i	$-0.720153\pi$
$643$	3.35759	−	3.35759i	0.132410	−	0.132410i	0.770206	+	0.637795i	$0.220153\pi$
$644$		0			0
$645$	5.67373	−	6.67608i	0.223403	−	0.262870i
$646$		0			0
$647$	−16.2015	+	8.25507i	−0.636946	+	0.324540i	−0.742473	−	0.669876i	$-0.766347\pi$
$647$	−16.2015	+	8.25507i	−0.636946	+	0.324540i	0.105527	+	0.994416i	$0.466347\pi$
$648$		0			0
$649$			21.7975i			0.855626i
$650$		0			0
$651$		−	0.316243i		−	0.0123945i
$652$		0			0
$653$	−26.4145	+	13.4589i	−1.03368	+	0.526686i	−0.886647	−	0.462446i	$-0.846972\pi$
$653$	−26.4145	+	13.4589i	−1.03368	+	0.526686i	−0.147031	+	0.989132i	$0.546972\pi$
$654$		0			0
$655$	1.10131	−	14.4450i	0.0430316	−	0.564411i
$656$		0			0
$657$	0.719692	−	0.719692i	0.0280779	−	0.0280779i
$658$		0			0
$659$	27.3439	+	19.8665i	1.06517	+	0.773888i	0.975037	−	0.222042i	$-0.0712721\pi$
$659$	27.3439	+	19.8665i	1.06517	+	0.773888i	0.0901289	+	0.995930i	$0.471272\pi$
$660$		0			0
$661$	2.34971	−	1.70716i	0.0913932	−	0.0664010i	−0.541150	−	0.840926i	$-0.682011\pi$
$661$	2.34971	−	1.70716i	0.0913932	−	0.0664010i	0.632543	+	0.774525i	$0.282011\pi$
$662$		0			0
$663$	2.43160	−	0.385127i	0.0944355	−	0.0149571i
$664$		0			0
$665$	−0.723976	−	0.843482i	−0.0280746	−	0.0327088i
$666$		0			0
$667$	11.7669	−	23.0938i	0.455616	−	0.894197i
$668$		0			0
$669$	10.0440	−	3.26351i	0.388325	−	0.126174i
$670$		0			0
$671$	23.4172	+	7.60872i	0.904012	+	0.293731i
$672$		0			0
$673$	25.6426	+	4.06138i	0.988449	+	0.156555i	0.629666	−	0.776866i	$-0.283192\pi$
$673$	25.6426	+	4.06138i	0.988449	+	0.156555i	0.358783	+	0.933421i	$0.383192\pi$
$674$		0			0
$675$	−15.9610	−	21.7440i	−0.614340	−	0.836928i
$676$		0			0
$677$	−0.209997	+	1.32587i	−0.00807086	+	0.0509574i	−0.991395	−	0.130904i	$-0.958212\pi$
$677$	−0.209997	+	1.32587i	−0.00807086	+	0.0509574i	0.983324	+	0.181861i	$0.0582121\pi$
$678$		0			0
$679$	−0.542265	+	1.66892i	−0.0208102	+	0.0640472i
$680$		0			0
$681$	1.32706	+	4.08427i	0.0508530	+	0.156509i
$682$		0			0
$683$	−28.3352	−	14.4375i	−1.08422	−	0.552436i	−0.181815	−	0.983333i	$-0.558197\pi$
$683$	−28.3352	−	14.4375i	−1.08422	−	0.552436i	−0.902401	+	0.430897i	$0.858197\pi$
$684$		0			0
$685$	−3.65766	+	15.4011i	−0.139752	+	0.588445i
$686$		0			0
$687$	−0.473878	−	2.99195i	−0.0180796	−	0.114150i
$688$		0			0
$689$	−10.4254	−	14.3493i	−0.397175	−	0.546665i
$690$		0			0
$691$	−17.4158	+	23.9708i	−0.662530	+	0.911894i	−0.999562	−	0.0295992i	$-0.990577\pi$
$691$	−17.4158	+	23.9708i	−0.662530	+	0.911894i	0.337032	+	0.941493i	$0.390577\pi$
$692$		0			0
$693$	0.0537344	+	0.0537344i	0.00204120	+	0.00204120i
$694$		0			0
$695$	−3.97219	−	16.3689i	−0.150674	−	0.620907i
$696$		0			0
$697$	0.686957	+	1.34823i	0.0260204	+	0.0510678i
$698$		0			0
$699$	13.1959			0.499114
$700$		0			0
$701$	19.4462			0.734472			0.367236	−	0.930128i	$-0.380304\pi$
$701$	19.4462			0.734472			0.367236	+	0.930128i	$0.380304\pi$
$702$		0			0
$703$	−9.11553	−	17.8902i	−0.343799	−	0.674743i
$704$		0			0
$705$	4.03254	−	2.48473i	0.151874	−	0.0935803i
$706$		0			0
$707$	1.64250	+	1.64250i	0.0617726	+	0.0617726i
$708$		0			0
$709$	18.2726	−	25.1500i	0.686241	−	0.944529i	−0.313747	−	0.949507i	$-0.601584\pi$
$709$	18.2726	−	25.1500i	0.686241	−	0.944529i	0.999988	+	0.00497747i	$0.00158439\pi$
$710$		0			0
$711$	0.257817	+	0.354854i	0.00966888	+	0.0133081i
$712$		0			0
$713$	−1.22160	−	7.71288i	−0.0457493	−	0.288850i
$714$		0			0
$715$	−3.58041	−	8.58444i	−0.133900	−	0.321040i
$716$		0			0
$717$	12.6587	+	6.44991i	0.472747	+	0.240876i
$718$		0			0
$719$	−3.81150	−	11.7306i	−0.142145	−	0.437477i	0.854488	−	0.519471i	$-0.173871\pi$
$719$	−3.81150	−	11.7306i	−0.142145	−	0.437477i	−0.996633	+	0.0819940i	$0.973871\pi$
$720$		0			0
$721$	−0.390443	+	1.20166i	−0.0145408	+	0.0447521i
$722$		0			0
$723$	5.18551	−	32.7400i	0.192851	−	1.21761i
$724$		0			0
$725$	11.6072	+	22.5077i	0.431082	+	0.835914i
$726$		0			0
$727$	−10.7519	−	1.70294i	−0.398767	−	0.0631585i	−0.0461698	−	0.998934i	$-0.514702\pi$
$727$	−10.7519	−	1.70294i	−0.398767	−	0.0631585i	−0.352598	+	0.935775i	$0.614702\pi$
$728$		0			0
$729$	27.4886	+	8.93158i	1.01810	+	0.330799i
$730$		0			0
$731$	1.89575	−	0.615968i	0.0701170	−	0.0227824i
$732$		0			0
$733$	15.7463	−	30.9039i	0.581603	−	1.14146i	−0.393420	−	0.919359i	$-0.628708\pi$
$733$	15.7463	−	30.9039i	0.581603	−	1.14146i	0.975023	−	0.222102i	$-0.0712917\pi$
$734$		0			0
$735$	2.09222	+	25.7780i	0.0771725	+	0.950836i
$736$		0			0
$737$	32.3931	−	5.13057i	1.19322	−	0.188987i
$738$		0			0
$739$	25.3653	−	18.4289i	0.933076	−	0.677920i	−0.0136677	−	0.999907i	$-0.504351\pi$
$739$	25.3653	−	18.4289i	0.933076	−	0.677920i	0.946744	+	0.321987i	$0.104351\pi$
$740$		0			0
$741$	−9.39125	−	6.82315i	−0.344996	−	0.250655i
$742$		0			0
$743$	−23.5771	+	23.5771i	−0.864959	+	0.864959i	−0.991909	−	0.126950i	$-0.959481\pi$
$743$	−23.5771	+	23.5771i	−0.864959	+	0.864959i	0.126950	+	0.991909i	$0.459481\pi$
$744$		0			0
$745$	−8.55462	−	3.51895i	−0.313417	−	0.128925i
$746$		0			0
$747$	0.703881	−	0.358645i	0.0257537	−	0.0131221i
$748$		0			0
$749$			1.97086i			0.0720136i
$750$		0			0
$751$			26.9305i			0.982710i	0.870960	+	0.491355i	$0.163498\pi$
$751$			26.9305i			0.982710i	−0.870960	+	0.491355i	$0.836502\pi$
$752$		0			0
$753$	18.3001	−	9.32435i	0.666891	−	0.339798i
$754$		0			0
$755$	34.8399	+	14.3315i	1.26795	+	0.521575i
$756$		0			0
$757$	−19.9611	+	19.9611i	−0.725500	+	0.725500i	−0.969720	−	0.244220i	$-0.921468\pi$
$757$	−19.9611	+	19.9611i	−0.725500	+	0.725500i	0.244220	+	0.969720i	$0.421468\pi$
$758$		0			0
$759$	−16.1610	−	11.7417i	−0.586609	−	0.426196i
$760$		0			0
$761$	32.3921	−	23.5343i	1.17421	−	0.853116i	0.182707	−	0.983167i	$-0.441514\pi$
$761$	32.3921	−	23.5343i	1.17421	−	0.853116i	0.991507	+	0.130051i	$0.0415141\pi$
$762$		0			0
$763$	0.909705	−	0.144083i	0.0329335	−	0.00521616i
$764$		0			0
$765$	−0.0392583	−	0.483698i	−0.00141939	−	0.0174881i
$766$		0			0
$767$	−7.40808	+	14.5392i	−0.267490	+	0.524979i
$768$		0			0
$769$	44.1316	−	14.3392i	1.59143	−	0.517086i	0.626458	−	0.779455i	$-0.284504\pi$
$769$	44.1316	−	14.3392i	1.59143	−	0.517086i	0.964968	+	0.262369i	$0.0845038\pi$
$770$		0			0
$771$	15.0852	+	4.90147i	0.543279	+	0.176522i
$772$		0			0
$773$	23.3059	+	3.69129i	0.838255	+	0.132767i	0.560779	−	0.827966i	$-0.310502\pi$
$773$	23.3059	+	3.69129i	0.838255	+	0.132767i	0.277477	+	0.960732i	$0.410502\pi$
$774$		0			0
$775$	6.81517	+	3.43062i	0.244808	+	0.123232i
$776$		0			0
$777$	0.163866	−	1.03461i	0.00587867	−	0.0371165i
$778$		0			0
$779$	2.20475	−	6.78552i	0.0789934	−	0.243117i
$780$		0			0
$781$	3.58302	+	11.0274i	0.128210	+	0.394591i
$782$		0			0
$783$	−24.3452	−	12.4045i	−0.870026	−	0.443300i
$784$		0			0
$785$	19.1413	+	45.8935i	0.683184	+	1.63801i
$786$		0			0
$787$	−2.02526	−	12.7870i	−0.0721926	−	0.455806i	−0.997131	−	0.0756899i	$-0.975884\pi$
$787$	−2.02526	−	12.7870i	−0.0721926	−	0.455806i	0.924939	−	0.380116i	$-0.124116\pi$
$788$		0			0
$789$	31.3697	+	43.1767i	1.11679	+	1.53713i
$790$		0			0
$791$	−0.971687	+	1.33741i	−0.0345492	+	0.0475529i
$792$		0			0
$793$	13.0337	+	13.0337i	0.462839	+	0.462839i
$794$		0			0
$795$	31.6872	−	19.5247i	1.12383	−	0.692469i
$796$		0			0
$797$	−20.9531	−	41.1228i	−0.742198	−	1.45665i	−0.884362	−	0.466802i	$-0.845406\pi$
$797$	−20.9531	−	41.1228i	−0.742198	−	1.45665i	0.142164	−	0.989843i	$-0.454594\pi$
$798$		0			0
$799$	1.07763			0.0381239
$800$		0			0
$801$	−2.70264			−0.0954930
$802$		0			0
$803$	4.22813	+	8.29818i	0.149208	+	0.292836i
$804$		0			0
$805$	−0.337694	−	1.39159i	−0.0119021	−	0.0490473i
$806$		0			0
$807$	−19.8082	−	19.8082i	−0.697280	−	0.697280i
$808$		0			0
$809$	−12.7018	+	17.4825i	−0.446571	+	0.614652i	−0.971656	−	0.236397i	$-0.924033\pi$
$809$	−12.7018	+	17.4825i	−0.446571	+	0.614652i	0.525086	+	0.851049i	$0.324033\pi$
$810$		0			0
$811$	26.8810	+	36.9985i	0.943918	+	1.29919i	0.954176	+	0.299245i	$0.0967347\pi$
$811$	26.8810	+	36.9985i	0.943918	+	1.29919i	−0.0102581	+	0.999947i	$0.503265\pi$
$812$		0			0
$813$	8.04203	+	50.7754i	0.282046	+	1.78077i
$814$		0			0
$815$	−0.903374	+	3.80378i	−0.0316438	+	0.133241i
$816$		0			0
$817$	−8.37434	−	4.26694i	−0.292981	−	0.149281i
$818$		0			0
$819$	0.0175793	+	0.0541035i	0.000614271	+	0.00189053i
$820$		0			0
$821$	−4.17662	+	12.8543i	−0.145765	+	0.448619i	−0.997109	−	0.0759897i	$-0.975788\pi$
$821$	−4.17662	+	12.8543i	−0.145765	+	0.448619i	0.851343	+	0.524609i	$0.175788\pi$
$822$		0			0
$823$	4.59531	−	29.0136i	0.160182	−	1.01135i	−0.768331	−	0.640053i	$-0.778913\pi$
$823$	4.59531	−	29.0136i	0.160182	−	1.01135i	0.928513	−	0.371299i	$-0.121087\pi$
$824$		0			0
$825$	18.5330	−	6.12211i	0.645236	−	0.213144i
$826$		0			0
$827$	−48.6187	−	7.70044i	−1.69064	−	0.267771i	−0.764408	−	0.644733i	$-0.776969\pi$
$827$	−48.6187	−	7.70044i	−1.69064	−	0.267771i	−0.926229	+	0.376962i	$0.876969\pi$
$828$		0			0
$829$	16.3509	+	5.31274i	0.567892	+	0.184519i	0.578869	−	0.815421i	$-0.303494\pi$
$829$	16.3509	+	5.31274i	0.567892	+	0.184519i	−0.0109774	+	0.999940i	$0.503494\pi$
$830$		0			0
$831$	−31.3416	+	10.1835i	−1.08723	+	0.353262i
$832$		0			0
$833$	−2.67132	+	5.24277i	−0.0925559	+	0.181651i
$834$		0			0
$835$	10.0796	+	11.7434i	0.348817	+	0.406396i
$836$		0			0
$837$	−8.13081	+	1.28779i	−0.281042	+	0.0445126i
$838$		0			0
$839$	28.7069	−	20.8568i	0.991074	−	0.720057i	0.0309178	−	0.999522i	$-0.490157\pi$
$839$	28.7069	−	20.8568i	0.991074	−	0.720057i	0.960156	+	0.279465i	$0.0901570\pi$
$840$		0			0
$841$	−2.70784	−	1.96736i	−0.0933738	−	0.0678400i
$842$		0			0
$843$	3.38429	−	3.38429i	0.116561	−	0.116561i
$844$		0			0
$845$	−1.68052	+	22.0420i	−0.0578115	+	0.758268i
$846$		0			0
$847$	0.606968	−	0.309265i	0.0208557	−	0.0106265i
$848$		0			0
$849$		−	52.2448i		−	1.79304i
$850$		0			0
$851$		−	25.8662i		−	0.886683i
$852$		0			0
$853$	14.2266	−	7.24881i	0.487109	−	0.248194i	−0.193146	−	0.981170i	$-0.561869\pi$
$853$	14.2266	−	7.24881i	0.487109	−	0.248194i	0.680255	+	0.732976i	$0.261869\pi$
$854$		0			0
$855$	−1.48181	+	1.74359i	−0.0506768	+	0.0596295i
$856$		0			0
$857$	−4.29173	+	4.29173i	−0.146603	+	0.146603i	−0.776598	−	0.629996i	$-0.783057\pi$
$857$	−4.29173	+	4.29173i	−0.146603	+	0.146603i	0.629996	+	0.776598i	$0.283057\pi$
$858$		0			0
$859$	−3.01819	−	2.19284i	−0.102979	−	0.0748187i	0.535104	−	0.844786i	$-0.320272\pi$
$859$	−3.01819	−	2.19284i	−0.102979	−	0.0748187i	−0.638083	+	0.769967i	$0.720272\pi$
$860$		0			0
$861$	0.301132	−	0.218785i	0.0102625	−	0.00745618i
$862$		0			0
$863$	−27.8172	+	4.40580i	−0.946907	+	0.149975i	−0.610744	−	0.791828i	$-0.709129\pi$
$863$	−27.8172	+	4.40580i	−0.946907	+	0.149975i	−0.336163	+	0.941804i	$0.609129\pi$
$864$		0			0
$865$	8.33140	−	13.6705i	0.283276	−	0.464812i
$866$		0			0
$867$	12.2473	−	24.0366i	0.415939	−	0.816326i
$868$		0			0
$869$	−3.81714	+	1.24026i	−0.129488	+	0.0420731i
$870$		0			0
$871$	23.3502	+	7.58696i	0.791193	+	0.257074i
$872$		0			0
$873$	3.56783	+	0.565088i	0.120753	+	0.0191253i
$874$		0			0
$875$	1.29653	+	0.525930i	0.0438307	+	0.0177797i
$876$		0			0
$877$	−0.589305	+	3.72072i	−0.0198994	+	0.125640i	−0.995638	−	0.0932978i	$-0.970259\pi$
$877$	−0.589305	+	3.72072i	−0.0198994	+	0.125640i	0.975739	+	0.218938i	$0.0702591\pi$
$878$		0			0
$879$	7.48668	−	23.0416i	0.252520	−	0.777175i
$880$		0			0
$881$	−6.17082	−	18.9918i	−0.207900	−	0.639851i	−0.999582	−	0.0289169i	$-0.990794\pi$
$881$	−6.17082	−	18.9918i	−0.207900	−	0.639851i	0.791682	−	0.610934i	$-0.209206\pi$
$882$		0			0
$883$	−0.994033	−	0.506485i	−0.0334519	−	0.0170446i	0.437185	−	0.899372i	$-0.355976\pi$
$883$	−0.994033	−	0.506485i	−0.0334519	−	0.0170446i	−0.470636	+	0.882327i	$0.655976\pi$
$884$		0			0
$885$	−29.2395	−	17.8198i	−0.982877	−	0.599006i
$886$		0			0
$887$	−0.00506085	−	0.0319529i	−0.000169927	−	0.00107287i	0.987603	−	0.156971i	$-0.0501729\pi$
$887$	−0.00506085	−	0.0319529i	−0.000169927	−	0.00107287i	−0.987773	+	0.155898i	$0.950173\pi$
$888$		0			0
$889$	−0.473355	−	0.651517i	−0.0158758	−	0.0218512i
$890$		0			0
$891$	−11.3071	+	15.5629i	−0.378803	+	0.521378i
$892$		0			0
$893$	−3.59294	−	3.59294i	−0.120233	−	0.120233i
$894$		0			0
$895$	−31.7549	−	26.9872i	−1.06145	−	0.902082i
$896$		0			0
$897$	−6.78908	−	13.3243i	−0.226681	−	0.444886i
$898$		0			0
$899$	7.72891			0.257774
$900$		0			0
$901$	8.46789			0.282106
$902$		0			0
$903$	−0.222607	−	0.436891i	−0.00740790	−	0.0145388i
$904$		0			0
$905$	−11.9341	−	0.909873i	−0.396702	−	0.0302452i
$906$		0			0
$907$	32.8325	+	32.8325i	1.09019	+	1.09019i	0.995508	+	0.0946771i	$0.0301819\pi$
$907$	32.8325	+	32.8325i	1.09019	+	1.09019i	0.0946771	+	0.995508i	$0.469818\pi$
$908$		0			0
$909$	2.81057	−	3.86841i	0.0932206	−	0.128307i
$910$		0			0
$911$	−18.2810	−	25.1617i	−0.605677	−	0.833643i	0.390536	−	0.920588i	$-0.372290\pi$
$911$	−18.2810	−	25.1617i	−0.605677	−	0.833643i	−0.996213	+	0.0869445i	$0.972290\pi$
$912$		0			0
$913$	1.13081	+	7.13967i	0.0374244	+	0.236289i
$914$		0			0
$915$	−29.3504	+	25.1920i	−0.970295	+	0.832823i
$916$		0			0
$917$	−0.722398	−	0.368080i	−0.0238557	−	0.0121551i
$918$		0			0
$919$	−0.0359360	−	0.110600i	−0.00118542	−	0.00364835i	0.950462	−	0.310841i	$-0.100611\pi$
$919$	−0.0359360	−	0.110600i	−0.00118542	−	0.00364835i	−0.951647	+	0.307192i	$0.900611\pi$
$920$		0			0
$921$	−14.3700	+	44.2263i	−0.473508	+	1.45731i
$922$		0			0
$923$	−1.35785	+	8.57312i	−0.0446941	+	0.282188i
$924$		0			0
$925$	20.5187	+	14.7549i	0.674650	+	0.485138i
$926$		0			0
$927$	2.56891	+	0.406876i	0.0843742	+	0.0133636i
$928$		0			0
$929$	10.2285	+	3.32343i	0.335585	+	0.109038i	0.471962	−	0.881619i	$-0.343546\pi$
$929$	10.2285	+	3.32343i	0.335585	+	0.109038i	−0.136377	+	0.990657i	$0.543546\pi$
$930$		0			0
$931$	26.3864	−	8.57346i	0.864779	−	0.280984i
$932$		0			0
$933$	22.7575	−	44.6642i	0.745049	−	1.46224i
$934$		0			0
$935$	4.32041	+	1.02607i	0.141293	+	0.0335561i
$936$		0			0
$937$	−1.19736	+	0.189643i	−0.0391160	+	0.00619537i	−0.175962	−	0.984397i	$-0.556304\pi$
$937$	−1.19736	+	0.189643i	−0.0391160	+	0.00619537i	0.136846	+	0.990592i	$0.456304\pi$
$938$		0			0
$939$	15.6966	−	11.4042i	0.512238	−	0.372163i
$940$		0			0
$941$	−38.2557	−	27.7944i	−1.24710	−	0.906072i	−0.249051	−	0.968490i	$-0.580119\pi$
$941$	−38.2557	−	27.7944i	−1.24710	−	0.906072i	−0.998050	+	0.0624187i	$0.980119\pi$
$942$		0			0
$943$	6.49920	−	6.49920i	0.211643	−	0.211643i
$944$		0			0
$945$	−1.46700	+	0.355992i	−0.0477215	+	0.0115804i
$946$		0			0
$947$	−37.4707	+	19.0923i	−1.21763	+	0.620415i	−0.940296	−	0.340358i	$-0.889452\pi$
$947$	−37.4707	+	19.0923i	−1.21763	+	0.620415i	−0.277337	+	0.960773i	$0.589452\pi$
$948$		0			0
$949$			6.97195i			0.226319i
$950$		0			0
$951$			4.00474i			0.129863i
$952$		0			0
$953$	−5.54476	+	2.82519i	−0.179612	+	0.0915170i	−0.541485	−	0.840711i	$-0.682138\pi$
$953$	−5.54476	+	2.82519i	−0.179612	+	0.0915170i	0.361872	+	0.932228i	$0.382138\pi$
$954$		0			0
$955$	27.9097	+	45.2955i	0.903137	+	1.46573i
$956$		0			0
$957$	13.9804	−	13.9804i	0.451921	−	0.451921i
$958$		0			0
$959$	0.716712	+	0.520722i	0.0231438	+	0.0168150i
$960$		0			0
$961$	−23.1956	+	16.8526i	−0.748246	+	0.543633i
$962$		0			0
$963$	4.00710	−	0.634662i	0.129127	−	0.0204517i
$964$		0			0
$965$	6.76920	−	2.82331i	0.217908	−	0.0908856i
$966$		0			0
$967$	−25.7210	+	50.4803i	−0.827132	+	1.62334i	−0.0460252	+	0.998940i	$0.514655\pi$
$967$	−25.7210	+	50.4803i	−0.827132	+	1.62334i	−0.781107	+	0.624398i	$0.785345\pi$
$968$		0			0
$969$	5.27077	−	1.71258i	0.169322	−	0.0550159i
$970$		0			0
$971$	22.5479	+	7.32627i	0.723598	+	0.235111i	0.647583	−	0.761995i	$-0.275780\pi$
$971$	22.5479	+	7.32627i	0.723598	+	0.235111i	0.0760156	+	0.997107i	$0.475780\pi$
$972$		0			0
$973$	−0.931076	−	0.147468i	−0.0298489	−	0.00472760i
$974$		0			0
$975$	14.4424	+	2.21509i	0.462526	+	0.0709397i
$976$		0			0
$977$	6.00177	−	37.8937i	0.192014	−	1.21233i	−0.683797	−	0.729672i	$-0.739673\pi$
$977$	6.00177	−	37.8937i	0.192014	−	1.21233i	0.875811	−	0.482654i	$-0.160327\pi$
$978$		0			0
$979$	7.64205	−	23.5198i	0.244241	−	0.751696i
$980$		0			0
$981$	−0.585892	−	1.80319i	−0.0187061	−	0.0575715i
$982$		0			0
$983$	−24.4725	−	12.4694i	−0.780551	−	0.397711i	0.0178471	−	0.999841i	$-0.494319\pi$
$983$	−24.4725	−	12.4694i	−0.780551	−	0.397711i	−0.798398	+	0.602130i	$0.794319\pi$
$984$		0			0
$985$	−35.2903	+	2.86426i	−1.12444	+	0.0912630i
$986$		0			0
$987$	−0.0414686	−	0.261822i	−0.00131996	−	0.00833389i
$988$		0			0
$989$	−7.11683	−	9.79548i	−0.226302	−	0.311478i
$990$		0			0
$991$	−12.3597	+	17.0116i	−0.392618	+	0.540393i	−0.958872	−	0.283838i	$-0.908392\pi$
$991$	−12.3597	+	17.0116i	−0.392618	+	0.540393i	0.566254	+	0.824231i	$0.308392\pi$
$992$		0			0
$993$	−23.8693	−	23.8693i	−0.757468	−	0.757468i
$994$		0			0
$995$	9.10893	−	22.1439i	0.288772	−	0.702009i
$996$		0			0
$997$	−15.4380	−	30.2987i	−0.488925	−	0.959569i	−0.995262	−	0.0972334i	$-0.969001\pi$
$997$	−15.4380	−	30.2987i	−0.488925	−	0.959569i	0.506337	−	0.862336i	$-0.330999\pi$
$998$		0			0
$999$	−27.2678			−0.862715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.d.223.6	yes	64
4.3	odd	2		800.2.bq.c.223.3	✓	64
25.12	odd	20		800.2.bq.c.287.3	yes	64
100.87	even	20	inner	800.2.bq.d.287.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.c.223.3	✓	64	4.3	odd	2
800.2.bq.c.287.3	yes	64	25.12	odd	20
800.2.bq.d.223.6	yes	64	1.1	even	1	trivial
800.2.bq.d.287.6	yes	64	100.87	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.751816 + 1.47552i) q^{3} +(-0.850652 + 2.06794i) q^{5} +(0.0884893 + 0.0884893i) q^{7} +(0.151419 - 0.208410i) q^{9} +(1.38554 + 1.90703i) q^{11} +(0.276048 + 1.74290i) q^{13} +(-3.69083 + 0.299558i) q^{15} +(-0.750646 - 0.382473i) q^{17} +(1.22753 + 3.77794i) q^{19} +(-0.0640402 + 0.197096i) q^{21} +(-0.800533 + 5.05437i) q^{23} +(-3.55278 - 3.51820i) q^{25} +(5.32824 + 0.843910i) q^{27} +(-4.81698 - 1.56513i) q^{29} +(-1.45130 + 0.471555i) q^{31} +(-1.77220 + 3.47813i) q^{33} +(-0.258265 + 0.107717i) q^{35} +(-4.99237 + 0.790713i) q^{37} +(-2.36415 + 1.71766i) q^{39} +(-1.45307 - 1.05572i) q^{41} +(-1.67304 + 1.67304i) q^{43} +(0.302175 + 0.490409i) q^{45} +(-1.13972 + 0.580715i) q^{47} -6.98434i q^{49} -1.39514i q^{51} +(-8.95574 + 4.56318i) q^{53} +(-5.12225 + 1.24300i) q^{55} +(-4.65156 + 4.65156i) q^{57} +(7.48107 + 5.43532i) q^{59} +(8.45057 - 6.13970i) q^{61} +(0.0318410 - 0.00504312i) q^{63} +(-3.83904 - 0.911749i) q^{65} +(6.31654 - 12.3969i) q^{67} +(-8.05968 + 2.61875i) q^{69} +(4.67813 + 1.52002i) q^{71} +(3.90231 + 0.618064i) q^{73} +(2.52014 - 7.88725i) q^{75} +(-0.0461465 + 0.291358i) q^{77} +(-0.526155 + 1.61934i) q^{79} +(2.52183 + 7.76139i) q^{81} +(2.73237 + 1.39221i) q^{83} +(1.42947 - 1.22694i) q^{85} +(-1.31210 - 8.28425i) q^{87} +(-6.16660 - 8.48760i) q^{89} +(-0.129801 + 0.178655i) q^{91} +(-1.78690 - 1.78690i) q^{93} +(-8.85676 - 0.675253i) q^{95} +(6.36605 + 12.4941i) q^{97} +0.607241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43}+ \cdots + 132 q^{99}+O(q^{100}) \) 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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